$\forall$$r$:Rng, $n$:$\mathbb{N}^{+}$, $e$:$\mid$$r$$\mid$. ($e$ $\uparrow$$r$ $n$) = (($e$ $\uparrow$$r$ ($n$ {-} 1)) $\ast$ $e$) $\in$ $\mid$$r$$\mid$